Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.3 7.2 7.3 6.3 8.1 6.8 7.0 7.1 6.8 6.5 7.0 6.3 7.9 9.0 9.0 8.7 7.8 9.7 7.4 7.7 9.7 7.9 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.8 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 9.0 7.6 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.8 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean ?1 and standard deviation ?1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean ?2 and standard deviation ?2. (a) Calculate the estimate for the given data. (Round your answer to three decimal places.) (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). V(X − Y) = V(X) + V(Y) = ?X2 + ?Y2 = n1 + ?22 ?X − Y = V(X − Y) = n1 + ?22 Compute the estimated standard error. (Round your answer to three decimal places.) (c) Calculate a point estimate of the ratio ?1/?2 of the two standard deviations. (Round your answer to three decimal places.) (d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X − Y between beam strength and cylinder strength. (Round your answer to two decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

5.3	7.2	7.3	6.3	8.1	6.8	7.0	7.1	6.8	6.5	7.0	6.3	7.9	9.0
9.0	8.7	7.8	9.7	7.4	7.7	9.7	7.9	7.7	11.6	11.3	11.8	10.7

The data below give accompanying strength observations for cylinders.

6.8	5.8	7.8	7.1	7.2	9.2	6.6	8.3	7.0	9.0
7.6	8.1	7.4	8.5	8.9	9.8	9.7	14.1	12.6	11.8

Prior to obtaining data, denote the beam strengths by X₁, . . . , X_m and the cylinder strengths by Y₁, . . . , Y_n. Suppose that the X_i's constitute a random sample from a distribution with mean ?₁ and standard deviation ?₁ and that the Y_i's form a random sample (independent of the X_i's) from another distribution with mean ?₂ and standard deviation ?₂.

(a) Calculate the estimate for the given data. (Round your answer to three decimal places.)

(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a).

V(X − Y)

V(X) + V(Y)

?_X² + ?_Y²

n₁

?₂²

?_X − Y

V(X − Y)

n₁

?₂²

Compute the estimated standard error. (Round your answer to three decimal places.)

(c) Calculate a point estimate of the ratio ?₁/?₂ of the two standard deviations. (Round your answer to three decimal places.)

(d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X − Y between beam strength and cylinder strength. (Round your answer to two decimal places.)

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